We now investigate numerically how \(\mathtt {RSVD}\)  implemented with a power iteration impacts the performance of the stochastic Ho-Kalman Algorithm. Again we focus on example 4. Based on the results of the previous subsection, we fix the oversampling parameter in \(\mathtt {RSVD}\)  as \(l=10\) , and sweep \(q\)  from 1 to 4. The results are shown in Figures REF  and REF . We observe that the realization error decreases as the power parameter \(q\)  increases as indicated in Eq (REF ). In contrast to the oversampling parameter \(l\) , the runtime demonstrably increases with \(q\)  at an empirically linear rate. This trend is expected and analyzed in [1]}.
